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Stephen PudneyInstitute for Social and Economic Research

University of Essex

No. 2010-07

March 2010

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Perception and Retrospection: The dynamic consistency of responses to survey questions on wellbeing

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Perception and Retrospection:

The dynamic consistency of responses to survey

questions on wellbeing

Stephen Pudney

Institute for Social and Economic ResearchUniversity of Essex

This version January 2010

Abstract

Implementation of broad approaches to welfare analysis usually entails the use of ‘subjec-tive’ welfare indicators. We analyse BHPS data on financial wellbeing to determine whetherreported current and retrospective perceptions are consistent with each other and with theexistence of a common underlying wellbeing concept. We allow for adjustment of perceptionsin a vector ARMA model for panel data, with dependent variables observed ordinally andfind that current perceptions exhibit slow adjustment to changing circumstances and retro-spective assessments of past wellbeing are heavily contaminated by current circumstances,causing significant bias in measures of the level and change in welfare.

Keywords: Financial wellbeing, perceptions, dynamic adjustment, BHPS.

JEL codes: C23, C25, C33, C35, D84

Contact: ISER, University of Essex, Wivenhoe Park, Colchester, CO4 3SQ, UK; tel.+44(0)1206-873789; email spudney@essex.ac.uk

This work was supported by the Economic and Social Research Council through the MiSoC and ULSCCentres. Earlier versions were presented at seminars or conferences at the Universities of Manchester,Southampton and Essex; I am grateful to participants for helpful comments. Andrew Henley kindly gaveme access to his work on housing equity. I have benefited greatly from Monica Hernandez’ advice on thesimulated annealing algorithm.

1 Introduction

‘Objective’ measures like income and consumption expenditure are questionable empirical

indicators of wellbeing. As Sen (1982 chapter 4, 1985, 1999) and others have argued, mea-

sures of opulence like income and expenditure represent only partial intermediate stages in

the chain linking fundamental entitlements and endowments to final welfare outcomes. They

may not be satisfactory as welfare measures in themselves and an exclusive focus on them

obscures the underlying physical, social and economic conditions that ultimately generate

welfare outcomes. Because income and expenditure are limited to the monetised components

of economic activity, their relevance to wellbeing depends critically on the degree to which

the economy is market-based and on the system of regulation used to control market failures.

A further important problem is measurement error, which affects the extremes of the income

and expenditure distributions in particular (Meyer and Sullivan 2003, Nicoletti et al 2010,

Pudney and Francavilla 2006). Recognition of the shortcomings of income and expenditure

as welfare measures leads naturally to empirical approaches with broader scope and there is

now a large applied literature that attempts to make wider views of welfare operational, both

empirically and in policy terms (Sen 1985, UNDP 1990, Ravallion and Lokshin 2001, Clark

2006, Dolan and White 2007, Anand et al 2009). Nevertheless, there remains scepticism

about the difficulties of making the approach operational (Sugden 1993).

Increased conceptual scope generally brings with it a move from the ‘objectivity’ of

cash measures like income and expenditure to the ‘subjectivity’ of self-reported personal

assessments of specific aspects of wellbeing. It is important not to over-emphasise the dis-

tinction between ‘objective’ and ‘subjective’ measures, since responses to survey questions

about income and expenditure involve cognitive and behavioural processes on the part of

the respondent which introduce considerable subjectivity. Nevertheless, survey questions on

income and expenditure embody a clear cash metric and fairly definite accounting princi-

ples, which give respondents a tangible framework for dealing with the question. This also

1

exists for some ‘subjective’ questions, such as those eliciting expectations using the concept

of probability to guide responses (Dominitz and Manski 1997). In contrast, requests for

personal assessments of happiness, satisfaction and many other aspects of wellbeing are po-

tentially more problematic because the associated response scales lack the clarity provided

by the conceptual frameworks of income accounting and probability theory. The accuracy

and internal consistency of the process by which perceptions are formed and expressed is

therefore likely to be a bigger concern for ‘subjective’ wellbeing variables than for ‘objective’

ones, although it is clearly important for both.

Retrospection is often an important component of empirical analysis. The wellbeing

literature suggests some systematic biases in the differences between experienced utility as

recorded continuously in experimental settings and remembered utility defined as retrospec-

tive evaluations of the same reference period (Kahneman et al 1993). However, for policy

purposes, we are more interested in how welfare changes over time in response to a changing

socio-economic environment than in assessments of the average level of past welfare during

some past period, and memory may operate in a different way when evaluating change than

it does when evaluating average past welfare. For the analyst, there are two obvious ways of

measuring welfare change: either by comparing current wellbeing measured in successive pe-

riods, or by using survey questions which invite respondents to make their own comparisons

of the current and past state. Let tzs be the individual’s perception, formed at time t, of the

level of wellbeing at time s. If s = t, then tzs is the current perception of current wellbeing

and if t > s, tzs is a current perception of past wellbeing. A comparison of successive current

measures looks at tzt − t−1zt−1, while the respondent’s own retrospective comparison looks

at tzt − tzt−1. The choice between these two measures is not clear-cut. The former approach

requires longitudinal data, which are expensive and relatively scarce, while the latter can

be used in both longitudinal and cross-sectional surveys. Even when longitudinal data are

available, there is a case for using retrospective questions to reveal change over time, since

evidence suggests that assessments of current wellbeing and attitudes are strongly influenced

2

by transient changes of mood, emotion and survey context (Smallwood and Schooler 2006,

Kaheneman and Krueger 2006, Conti and Pudney 2008). This is a problem for comparison

of successive current measures, tzt − t−1zt−1, since each term in the difference is subject to

a different injection of noise, and the variance of the measured difference is consequently

inflated. Retrospective comparisons of the present and the past may be less affected: if mea-

surement noise is a fixed effect specific to the time of interview but common to the current

perception of both the present (tzt) and the past (tzt−1), then the respondent’s comparison

of the two eliminates noise completely.

Examples of econometric analysis of attitudinal variables have proliferated with the de-

velopment of the economic literature on happiness and satisfaction (Van Praag and Ferrer-

i-Carbonell, 2004, Layard 2006). This body of applied work analyses responses to survey

questions of the Likert (1932) type, where respondents are offered a pre-specified numerical

scale of responses. There has been important work on econometric methodology in this area

but, so far, little systematic discussion of the dynamics of perceptions, the intertemporal

consistency of responses, or the type of dynamic analysis most appropriate for the evolu-

tion of attitudes and perceptions over time. There are difficult technical issues involved in

econometric modelling of categorical variables. Discrete data may be either inherently dis-

crete (for example, an individual either has a job or not) or observationally discrete: when

the variables of interest are naturally continuous, but the survey instrument uses an ordinal

scale of permitted responses to impose discreteness artificially. The state dependence model

(Heckman 1978) and models of latent dynamics (Pudney 2008) are examples of econometric

approaches in these two cases. Perceptions of wellbeing are not inherently discrete and so the

more usual state dependence model is questionable. If the discrete nature of the dependent

variable is only an artificial construct imposed by the questionnaire designer, then behaviour

centres on the continuous latent perception of wellbeing which underlies the responses to

survey questions, rather than the responses themselves. The econometric approach devel-

oped and applied here is intended to uncover this underlying welfare variable and determine

3

whether respondents’ reporting of it displays the properties of temporal consistency that we

require of a good empirical welfare measure.

2 Panel evidence on perceptions of financial wellbeing

We use data from the British Household Panel Survey (BHPS), which is the principal source

of household- and individual-level panel data in the UK. Starting in 1991, it has followed all

original members of the sample annually, providing individual interviews with all over-15s

in the household. We use observations on 3768 individuals who were household reference

persons in the year 1992. The resulting panel dataset is unbalanced but has a common initial

period t = 0 in 1993. The year 1992 is lost through the need to construct certain differenced

variables and our sample period ends in 2003 to allow use of the housing equity variables

constructed by Henley (1998) and updated by him to 2003.

2.1 Question design

Each year, BHPS participants are asked a series of questions about their attitudes and

perceptions. For one of these domains, relating to a general concept of financial wellbeing

(FWB), we also have an additional retrospective question and a follow-up on the reasons for

the perceived change over time. The principal question relating to current FWB is:1

FWB1 How well would you say you yourself are managing financially these days? [(1)

finding it very difficult ; (2) finding it quite difficult ; (3) just about getting by ; (4) doing al-

right ; (5) living comfortably.]

In addition to the questions on FWB, there is also a group of BHPS satisfaction questions

which invites respondents to rate, on a 1-7 scale, their satisfaction with various aspects of

life, including satisfaction with income (SI) and with life overall (SLO).

1The item non-response/don’t know rate is only 0.14% for the full pooled sample covering the 1992-2003waves and we drop these few cases in the analysis that follows.

4

Sen’s (1982, 1985) capabilities analysis provides a possible framework for locating survey

questions like FWB1 and SLO in the spectrum of wellbeing concepts. In Sen’s approach, an

individual has command over economic resources (“entitlements”) represented by the set X

of possible choices for his or her commodity vector x.2 With a given vector of commodities,

the individual achieves a vector of “functionings” b via a utilisation function b = f(x). The

particular pattern of commodity utilisation is chosen from a set F of possible utilisation

functions. Sen (1985) equates the idea of “wellbeing” with an evaluation v(b) of the achieved

level of functionings3 and Anand et al (2009) take this further empirically by associating

the BHPS-type SLO variable with this concept of achieved wellbeing. Sen then contrasts

wellbeing with the broader concept of “advantage”, which introduces notions of freedom and

opportunity, through the capabilities set Q(X) defined as the set of life opportunities open

to the individual:

Q(X) = b : b = f(x), f(.) ∈ F, x ∈ X (1)

Personal advantage can then be thought of as an evaluation V (Q) of the set of possible

capabilities rather than the particular element of Q which is realised as an outcome. This

broader evaluation allows the possibility that freedom matters, in the sense that a given

outcome chosen from a restricted set of capabilities may be less rewarding4 than the same

outcome chosen from a wider set of possibilities.

However, the responses to survey questions on life satisfaction, financial wellbeing, etc.

are determined in practice by survey respondents, not by theoretical debate about the con-

cepts of wellbeing and advantage. So how do real people understand and interpret such

questions? It is not possible to be sure about this but it seems possible that survey respon-

dents, when asked about their life satisfaction or financial wellbeing in questions like SLO

2Commodities here include labour supplies, so X encompasses the trade-off between work and consump-tion. Sen also makes a distinction between commodities and their Gorman-Lancaster characteristics, whichwe leave implicit.

3The evaluation v(.) may or may not represent a complete ordering of the set b and it need not coincidewith happiness or utility.

4Or possibly more rewarding in some settings, since freedom of choice is not necessarily always a positiveattribute (Schwartz 2004).

5

and FWB1, take a broad view of what is wanted by the survey designer and give an answer

that evaluates not just the realised value of the functionings vector b or the commodity vec-

tor x, but also some aspects of the sets Q and X from which they are generated – in other

words, evaluations of feasible potential outcomes as well as actual outcomes.

If it is true that FWB1 is answered partly on the basis of command over resources rather

than the realised income-consumption position, we would expect FWB1 to have greater pre-

dictive power for SLO than do conventional measures of income. To explore this, we estimate

random effects ordered probit models for the two satisfaction variables SLO and SI, using

1992-2003 BHPS waves.5 These models have a wide range of covariates covering personal

and household characteristics and circumstances, together with three income variables (cur-

rent per capita gross income, the respondent’s share in household income, and the change

in household income since the previous year) and also four dummy variables representing

the response given to the financial wellbeing question FWB1. Table 1 reports Wald tests

for the hypotheses that: (i) the FWB dummies are irrelevant; and (ii) the income variables

are irrelevant. For comparison, Table 1 also gives results for the same model applied to the

responses from a third BHPS question, asking for an evaluation of satisfaction with income.

Table 1 Random effects ordered probit models of satisfactionwith life overall and income (BHPS): Wald tests ofFWB and income coefficients

Dependent variable H(1)0 : FWB irrelevant H

(2)0 : Income irrelevant

Satisfaction with life overall χ2(4) = 629.48 χ2(3) = 3.16(P = 0.000 ) (P = 0.367 )

Satisfaction with income χ2(4) = 4160.6 χ2(3) = 206.12(P = 0.000 ) (P = 0.000 )

See Appendix 2, Table A1, for full details of the model and coefficient estimates.

The response to FWB1 has much greater explanatory power as a predictor of the broad

SLO measure of wellbeing than income: the FWB1 dummies are highly significant, while

5Other modelling approaches, such as random effects and consitional logit for SLO converted into binaryform, give essentially the same conclusions.

6

the coefficients of the three income variables are not significantly different from zero in

a joint test. This is suggestive rather than conclusive, but it is consistent with the idea

that survey questions like FWB1 give an assessment of command over market resources

that is broader than income itself and includes some element of evaluation of the set X

of consumption/income possibilities rather than adequacy of current realised income alone.

Unsurprisingly, analysis of responses to the question on satisfaction with income does succeed

in finding significant income coefficients but, even there, they are dominated by FWB1 as a

predictor of income satisfaction.

2.2 Retrospective questions

The retrospective BHPS question on FWB is:6

FWB2 Would you say you yourself are better off or worse off financially than you were a

year ago? [(1) worse off ; (2) about the same; (3) better off.]

Those who report some change at FWB2 are then asked:

FWB3 Why is that?

The free text responses are coded ex post into eighteen specific categories and six “other”/

inapplicable/non-response categories.7

Just over half the responses to question FWB2 over the 1992-2003 period indicated no

change in wellbeing, a quarter indicated a deterioration and slightly fewer (23%) suggested

an improvement. Table 2 shows the distribution of reasons given by those reporting retro-

spectively an improvement or deterioration in wellbeing. Increased earnings and increased

expenditure commitments are the dominant reasons given by these two groups respectively.

6The item non-response/don’t know rate is 0.3% for the pooled 1992-2003 sample.7In our sample, of the 18,873 observations where this question is applicable, there was a 0.58% non-

response/don’t know rate.

7

However, the benefit system also plays an important role, since 11% of people reporting an

improvement attribute it primarily to the effect of social security benefits.

Table 2 Reasons specified for retrospective change in wellbeing

Retrospectiveassessment of Investment One-offchange since Earnings Benefits income Expenses payment

last year changed changed changed changed or receipt Other

Improved 50.5 11.3 3.6 15.3 3.5 15.9(n=9,086)

Worse 25.1 3.8 5.5 49.8 1.2 14.7(n=9,771)

Note: Row percentages; BHPS sample of individuals who were household reference persons

in 1992, using waves from 1992-2003

What is the ‘objective’ basis for these retrospective assessments? Table 3 compares

the stated reasons for change with the corresponding change in reported income over the

two years concerned. Five concepts of real gross income are used: the respondent’s personal

earnings, benefits, investment income and total income, together with total household income

expressed in per capita form. On average, the responses to FWB3 match actual change in

economic circumstances quite well: for example, those reporting diminished wellbeing on

grounds of a fall in earnings report a current level of annual earnings averaging almost

£2,000 below the level reported in the previous year.

8

Table 3 Comparison of mean actual real income changes with retrospectiveassessments of the change in wellbeing (standard errors in parentheses)

Actual income change (£per year)Retrospective assessment Respondent’s personal income Per capitaof change in wellbeing Investment Total household& reported cause Earnings Benefits income income incomeIncreased earnings 1,613 -87 50 1,535 1,814

(169) (17) (35) (182) (136)Increased benefits -181 1,001 89 1,082 1,024

(69) (65) (59) (132) (115)Increased investment 155 19 321 592 455income (242) (49) (247) (362) (411)No change 142 177 9 413 380

(52) (11) (13) (55) (39)Reduced earnings -1,990 346 22 -1,312 -2,003

(251) (35) (37) (253) (125)Reduced benefits -402 -653 12 -1128 294

(184) (187) (55) (266) (200)Reduced investment -139 116 -81 -86 258income (131) (46) (127) (206) (167)

Note: Full BHPS sample of individuals who were household reference persons in 1992, using waves from 1992-2003,various row sample sizes; standard errors in parentheses

Although Table 3 shows what one might expect for the relationship between retrospec-

tive assessments and mean income change, it conceals numerous conflicts at the individual

level. Table 4 shows that, among respondents who report an increased level of FWB by

virtue of an earnings change, over a quarter in fact reported no increase in either their own

personal earnings or total household earnings when answering detailed income questions.

Larger degrees of dissonance are evident for other income components, particularly invest-

ment income. Part of this apparent conflict might be attributable to the broad scope of the

FWB variable, which may be capturing changes in the individual’s economic situation not

reflected in short-term income movements, and some of the conflicts are undoubtedly due to

income measurement error.8 Nevertheless, this evidence casts some doubt on the validity of

retrospective FWB comparisons.

8It should be noted that income measurement error may also have the opposite effect of making someactual conflicts appear non-conflicting.

9

Table 4 Sample proportions of contradictions betweenretrospective direction and reason for changeand ‘objective’ change in household income

Retrospective Reported reason for FWB changedirection of Benefit Investment

change in FWB Earnings income incomeReported increase 25.3 27.7 52.9

(0.7) (1.4) (2.8)Reported decrease 28.3 30.7 35.7

(0.9) (2.5) (1.8)

BHPS 1992-2003 sample percentages of contradictions. Standard errors in parentheses.

2.3 Perceived current wellbeing

The sequence of current assessments given in response to FWB1 is summarised in Table A2

of Appendix 2, which shows the transition rates between FWB1 response states in successive

years. Higher states are more persistent than lower states: only a third of respondents remain

in the “very difficult” state in successive years, whereas two-thirds of people in the “living

comfortably” state remain there in the following year. Large transitions are quite rare, but

more frequent in an upward than a downward direction. Table 5 examines the incidence of

conflicts between the current and retrospective assessments of wellbeing. Given the coarser

classification used for FWB2 than for FWB1, one would expect to see some of the cases of

change in the current assessment to be reported as no change in the retrospective question,

because of the presumably wider “no change” interval used by respondents when answering

FWB2. This could account for the non-zero proportions in cells (1,2) and (3,2) of Table 5, but

the large entries in cells (1,3), (2,1), (2,3) and (3,1) are definitely contrary to expectations.

In particular, of those whose current assessment declines from year to year, almost one in

eight reports a contradictory improvement in the retrospective assessment and, among those

whose current assessment improves, one in six retrospectively reports a worsening of their

financial situation.

10

Table 5 Conflicts between current and retrospective responses

Change in current Retrospective assessment of change in wellbeing % oflevel of wellbeing Worse Same Better totalDecrease 43.7 44.4 11.9 20.3No change 22.4 54.9 22.7 56.2Increase 16.2 49.0 34.9 23.5% of total 25.3 51.4 23.3 100.0

Note: Row percentages; BHPS sample of individuals who were household referencepersons in 1992, using waves from 1992-2003, n = 37, 943)

3 Adjustment, adaptation and dynamic consistency of

perceptions

Two points emerge from the preceding descriptive analysis. One is that responses to the ret-

rospective questions FWB2 and FWB3 are coherent in an average sense, but with significant

conflict at the individual level between the changes in reported incomes and retrospective as-

sessments. The second is that there is substantial conflict between retrospective assessments

(FWB2) and the sequence of current assessments of wellbeing (FWB1). These conclusions

support the idea that some systematic revision of perceptions may happen over time, disrupt-

ing the relationship between self-reports and the underlying actual change in circumstances.

We investigate the issue using a latent perceptions model to investigate more formally the

temporal consistency of reported perceptions and consequently to determine whether there

exists a single underlying concept of financial wellbeing recoverable from longitudinal survey

data. We view the responses to questions FWB1 and FWB2 as ordinal indicators of under-

lying perceptions of wellbeing, where those perceptions are essentially continuous variables.

To capture this idea, we specify a dynamic model, permitting substantial deviations from

temporal consistency, and then examine the validity of the restrictions necessary to impose

consistency on that structure.

11

Questions FWB1 and FWB2 give us information relating to perceived current wellbeing,

tzt, and a current assessment of change, tzt− tzt−1. To use these survey questions to generate

indicators of wellbeing, there must exist a ‘true’ welfare measure for each period, ωt and

the sequences of perceptions tzt and tzt−1 must satisfy the relations tzt = ωt and tzt −

tzt−1 = ωt − ωt−1 for all t. It is axiomatic for conventional welfare analysis that wellbeing

is path-independent in the sense that, given a sufficiently complete specification of current

circumstances (entitlements, capabilities, etc.), the measure of welfare is independent of

the path by which those circumstances have been reached. For example, the equivalised

income or consumption measure used in conventional poverty and inequality analysis is path

independent, given current income and family structure. A more general way of embedding

path independence is to specify a static model for ωt, such as the regression structure:

ωt = x′

tψ + υ + ξt (2)

where xt is a vector of observed variables describing the individual’s characteristics, circum-

stances and embodied capitals, υ is a persistent individual-specific unobservable and ξt is the

time-varying unobservable component of wellbeing. In the absence of perception errors, this

gives the following 2-equation system with a moving average error structure for the (latent)

responses to FWB1 and FWB2:

tzt = x′

tψ + υ + ξt (3)

tzt − tzt−1 = (xt − xt−1)′ψ + ξt − ξt−1 (4)

To investigate temporal consistency, we need to specify a more general model allowing the

deviation of perceived from actual wellbeing. This is more complex than the specification of

conventional time-series models of temporal adjustment, since there are two time dimensions

here: the time at which the perception is expressed and the time to which that perception

relates.

12

A generalised partial adjustment model relates the realised year-to-year adjustment in

perceived current wellbeing, tzt − t−1zt−1, to the adjustment warranted by changing circum-

stances, (ωt − t−1zt−1):

tzt − t−1zt−1 = λ(ωt − t−1zt−1) + ∆x+it

′

δ1 + v1 + e1t (5)

where 0 ≤ λ ≤ 1 is a speed-of-adjustment parameter, x+it is a subvector of xit and ∆x+

it

captures any change in state variables (marital or health status, for example) that might

have a temporary impact on perceptions through emotional over- or under-reaction. If a

coefficient in δ1 has the opposite sign to the corresponding coefficient in ψ, the model

displays temporary under-reaction; if the same sign, there is temporary over-reaction. The

variables v1 and e1t are respectively persistent and transient unobserved elements of the

perception process and v1 might represent the individual’s idiosyncratic understanding of

the meaning of the response scale for FWB1. This generalises (3) to:

tzt = (1 − λ)t−1zt−1 + x′

tψλ + λυ + λξt + ∆x+it

′

δ1 + v1 + e1t (6)

Our model for the updating of perceptions relating to any fixed past period t − 1 captures

both partial adjustment of perceptions and cross-contamination between time periods:

tzt−1 − t−1zt−1 = φ(ωt−1 − t−1zt−1) + π(ωt − t−1zt−1) + ∆x+it

′

δ2 + v2 + e2t (7)

where φ(ωt−1 − t−1zt−1) represents delayed adjustment of perceptions towards the true level

ωt−1 and π(ωt − t−1zt−1) represents contamination of the perception of past FWB by current

circumstances ωt.9 The latter effect can be interpreted in various ways. It is consistent with

one form of the adaptation hypothesis (Diener et al 1999, Loewenstein and Ubel 2008), which

holds that the meaning respondents attach to the concept of wellbeing is itself changed by

experience. In (7), the term ωt refers to experience accumulated after period t − 1, which

9Equation (7) can be re-specified with the term ωt replaced by its perceived equivalent tzt, the onlydifference to the model being that the parameter π in equation (8) below is replaced by λπ throughout. Thenature of our conclusions is not affected.

13

might change the individual’s reference point. In this case, we would expect π < 0, since

adaptation to high current wellbeing would make the past appear worse and vice versa. The

term π(ωt − t−1zt−1) is also consistent with a different behavioural process which we call

memory substitution – if past wellbeing cannot be recalled reliably, the respondent may,

consciously or unconsciously, partially substitute current wellbeing, for which there is no

problem of recall. This would imply π > 0. The term ∆x+it

′

δ2 represents a temporary

reaction to changes of state and v2 and e2t are persistent and transient unobserved elements

of the retrospection process.

Assumptions (5) and (7) imply the following generalisation of (4):

(tzt − tzt−1) = (φ + π − λ) t−1zt−1 + x′

tψ(λ − π) − x′

t−1ψφ

−(φ + π − λ)υ + (λ − π)ξt − φξt−1 + e1t − e2t + ∆x+it

′

(δ1 − δ2) + v1 − v2 (8)

Dynamic consistency would require the restrictions λ = φ = 1, π = 0 and δ1 = δ2 = 0 to

be imposed. Perfect consistency, with no reporting error, would further require var(e1t) =

var(e2t) = var(v1) = var(v2) = 0, giving the degenerate model (3)-(4), but the absence of

even random perception errors seems an unduly demanding requirement.

In practice, an ordinal scale is used for observation and we assume responses are generated

by the conventional threshold-crossing mechanism:

y1it = r ⇔ tzt ∈ [Γ1r, Γ1

r−1) , r = 1...5 (9)

y2it = r ⇔ (tzt − tzt−1) ∈ [Γ2r, Γ2

r−1) , r = 1...3 (10)

where y1it and y2it are the ordinal responses to questions FWB1 and FWB2 and the Γjr are

threshold parameters, where Γ10 = Γ2

0 = −∞ and Γ15 = Γ2

3 = +∞. Since the scale and origin

of tzt and (tzt − tzt−1) are not identifiable, normalisations are required. We renormalise the

equations to give new threshold parameters Γ∗jr such that Γ∗1

1 = Γ∗21 = 0 and Γ∗1

2 = Γ∗22 = 1

so that the model becomes:

y∗

1it = (1 − θ1)y∗

1it−1 + x′

itθ4θ1 + θ1ζit + ∆x+it

′

θ5 + u1i + ε1it (11)

14

y∗

2it = (θ2 − θ3)y∗

1it−1 + x′

itθ4θ3 − x′

it−1θ4θ2 + θ3ζit − θ2ζit−1 + ∆x+it

′

θ6 + u2i + ε2it (12)

where y∗

1it = tzit/S1 and y∗

2it = (tzit − tzit−1)/S2 are the renormalised latent perceptions

underlying responses to FWB1 and FWB2, Sj = Γj2 − Γj

1 is the normalising factor for the

jth equation and the Γ∗jr are the pre-normalisation thresholds. This normalisation is more

convenient than, but observationally equivalent to, the more usual one of setting intercepts

to zero and residual variances to unity. The parameter vector for this form of the model

is [θ1, θ2, θ3,θ′

4,θ′

5,θ′

6] = [λ, (φS1/S2), ([λ − π]S1/S2), (ψ′/S1), (δ

′

1/S1), (δ1 − δ2)′/S2)], and

the composite unobservables are u1i = (λυ + v1)/S1, u2i = (v1 − v2 − (φ + π − λ)υ)/S2,

ε1it = e1it/S1, ε2it = (e1it−e2it)/S2 and ζit = ξit/S1. The lagged latent variable y∗

1it−1 appears

in both equations (11) and (12) but the lag of y∗

2it in neither, which greatly simplifies the

treatment of initial conditions. Detailed discussion of the general case of a multi-equation

dynamic system of ordinal variables with moving average errors is set out in Appendix 1,

where identification and estimation by maximum simulated likelihood (MSL) are explained.

4 Empirical analysis

This application is based on waves 2-13 of the BHPS, covering the years 1992-2003. We first

select a sample consisting of all individuals recorded as the household reference person in the

1992 wave. Those individuals are then observed for 1993 (period 0) through all subsequent

periods until 2003 (period T = 10) or an attrition event, whichever occurs sooner. This gives

an unbalanced but compact panel, containing 3,768 individuals and 32,698 observations in

total (averaging 8.7 observations per individual). The vector xit, which is summarised in

Table A3 of Appendix A2, contains covariates representing personal and household character-

istics, partnership status, education, income and housing equity, which is the dominant form

of wealth for the great majority of households. The covariates are broadly representative of

variables used in the empirical literature on subjective wellbeing.

15

4.1 Long-run effects

MSL estimates of the key parameters of the joint model (11) and (12) are set out in Tables

6-8 below and full estimates are given in Table A4 of Appendix 2. The estimated coeffi-

cient vector ψ/S1, which represents the long-run comparative statics effect of x on financial

wellbeing, is reproduced in Table 6. Estimated coefficients are consistent with expectations

and broadly in line with evidence from the applied literature on other measures of subjec-

tive wellbeing; in particular, there is a wide range of significant influences beyond income.

Wellbeing is found to be significantly increasing in real per capita household income and

also in the respondent’s own share of household income. The latter conflicts with the idea

of risk reduction by diversification but may reflect a subjective value placed on a sense of

financial control, which is consistent with Sen’s notion of the capabilities set as a basis of

welfare evaluation. There are also significant positive effects for education, interpretable as

an indicator of human capital, and for home ownership and housing equity, which provide

a measure of real physical assets and of access (through the financial markets) to a store of

potential finance for meeting future borrowing needs. Both of these are consistent with the

idea that subjective financial wellbeing represents Sen’s notion of “advantage”, involving an

evaluation of the entitlement set X rather than the current income-consumption outcome

alone.

Relationship status is a very strong influence on financial wellbeing. Relative to a baseline

of marriage or cohabitation, there are large, approximately equal, negative effects for single

(never married) status and widow(er)hood and a much larger negative effect for divorce.

There is no strongly significant evidence of an effect for household size or composition.

There is significant evidence of lower financial wellbeing for members of the two main ethnic

minority groups, which might be interpreted in line with Sen’s approach, as representing the

exclusion of minority groups from access to economic opportunity. However, the smaller but

significant gender effect favouring women is not consistent with that interpretation. Cohort

16

and year effects are captured in the model by a quadratic in year of birth and a set of year

dummies and there is a significant negative cohort effect (or, equivalently, a rising age profile)

and rising year effect.

Table 6 Long-run coefficients (ψ/S1)

Covariate Coefficient Covariate CoefficientHousehold income p.c.a 4.579∗∗∗ Female 0.140∗∗

(0.246) (0.055)

Share in household income 0.252∗∗∗ African/Caribbean −0.753∗∗

(0.086) (0.321)

Home-owner 0.629∗∗∗ South Asian −0.446∗∗

(0.069) (0.219)

Housing equityb 0.053∗∗∗ Single (never married) −0.398∗∗∗

(0.015) (0.089)

Private rented home 0.096 Divorced −0.687∗∗∗

(0.097) (0.087)

Employed −0.068 Widow(er) −0.382∗∗∗

(0.083) (0.096)

Self-employed −0.098 (Year of birth - 1940)/10 −0.246∗∗∗

(0.105) (0.028)

Retired −0.130 ((Year of birth - 1940)/10)2 0.013(0.123) (0.010)

Unemployed −0.619 1999c −0.343∗∗∗

(0.185) (0.071)

Long-term sick −0.453∗∗∗ 2000c −0.308∗∗∗

(0.124) (0.054)

University degree 0.329∗∗∗ 2001c −0.098∗∗∗

(0.080) (0.053)

Certificate/diploma 0.0.373∗∗∗ 2002c −0.102∗∗∗

(0.099) (0.055)

High school qualification 0.195∗∗ Pre-school child 0.234(A-level) (0.078) (0.234)

Intermediate school qualification 0.182∗∗∗ Number of pre-school children −0.146(O-level/GCSE) (0.065) (0.128)

Vocational qualification 0.034 Number of school-age children 0.001(0.052) (0.029)

Number of retired adults 0.061(0.074)

Number of other adults −0.063∗

(0.038)

a in £’000 per year; b in £00,000; c reference year 1999; standard errors in parentheses; Significance: ∗ = 10%; ∗∗ = 5%; ∗∗∗ = 1%

17

4.2 Evidence on temporal consistency

Our primary interest is in temporal consistency, which concerns the three critical dynamic

adjustment parameters whose estimates are reproduced in Table 7. In the equation (11) for

current wellbeing, the parameter λ governs the speed of adjustment of current perceptions to

changing circumstances. The estimate implies that only two-thirds of the warranted adjust-

ment is completed within a year and the hypothesis λ = 1 is strongly rejected by an asymp-

totic t-test. The estimate of equation (12) for FWB2 also implies substantial deviations

from temporal consistency. The normalised difference between the adjustment parameter

λ and the cross-period contamination parameter π is not significantly different from zero,

suggesting that π is also approximately 0.67. On its own, this term would imply that the

retrospective perception of last year’s wellbeing is a weighted average of current wellbeing

and last year’s current perception, with two-thirds of the weight given (inappropriately) to

current conditions. This is offset only partially by the significantly positive adjustment pa-

rameter φ, which tends to push the retrospective perception towards the true value ωt−1.

The positive sign of π gives the important conclusion that the contamination of retrospective

perceptions by current conditions arises from a process like memory substitution rather than

adaptation of the individual’s reference standard to more recently experienced conditions,

which would require π < 0.

Table 7 Dynamic adjustment parameters

Parameter EstimatePartial adjustment λ 0.665∗∗∗

(0.020)

Adjustment of perceptions φS1/S2 0.090∗∗

(0.036)

Adaptation of perceptions [λ − π]S1/S2 −0.028(0.025)

Standard errors in parentheses; Significance: ∗ = 10%; ∗∗ = 5%; ∗∗∗ = 1%

The coefficients of ∆x+it in the two equations of the model are set out in Table 8, with

estimates of corresponding long-run effects from ψ/S1 reproduced for comparison. A Wald

18

test strongly rejects the hypothesis δ1 = 0, with significant negative coefficients for job

loss and onset of poor health, which match the negative signs of their long-run effects and

imply short-term over-reaction to these events. The significant positive coefficients for the

level and change in real housing equity also imply that perceptions of current financial

wellbeing display very large short-term over-reaction to booms in the housing market, which

is consistent with some macro-economic evidence on the influence of house prices on consumer

behaviour (see Muellbauer and Murphy 2008 for a review). The only (marginally) significant

evidence of under-reaction is with respect to income, where the long-run income effect is

temporarily offset to some degree by a negative coefficient for income change.

The significant deviations from λ = 1 and δ1 = 0 have important implications for

empirical analysis, since they imply that cross-section estimates of a static model of current

wellbeing will be affected by misspecification bias. Although many cross-section surveys

include recall questions that allow inclusion of the term ∆x+′

δ1 representing transient effects

on perceived FWB of the arrival of a shock, λ 6= 1 implies gradual adjustment of perceptions

over a long period and thus requires panel data to allow for its effects.

19

Table 8 Transient effects of life events and changes inincome and housing equity

LR effect Transient effectsState ψ/S1 δ1/S1 (δ1 − δ2)/S2

Divorce/separationa −0.687∗∗∗ −0.188 −0.195∗∗∗

(0.087) (0.120) (0.071)

Widow(er)hooda −0.382∗∗∗ 0.162 0.029(0.096) (0.178) (0.106)

Retirement -0.130 −0.109 −0.284∗∗∗

(0.123) (0.100) (0.054)

Unemployment −0.619∗∗∗ −0.571∗∗∗ −0.506∗∗∗

(0.185) (0.173) (0.075)

Ill-health −0.453∗∗∗ −0.624∗∗∗ −0.066(0.124) (0.177) (0.103)

New-born child -0.146 -0.090 −0.211∗∗∗

(0.128) (0.111) (0.053)

Per capita real incomeb 0.046∗∗∗ −0.003∗ 0.009∗∗∗

(0.002) (0.001) (0.001)

Real housing equityc 0.053∗∗∗ 0.099∗∗ 0.158∗∗∗

(0.015) (0.050) (0.017)

χ28 Wald joint significance test 36.4∗∗∗ 230.8∗∗∗

a Baseline category = married/cohabiting; b = in £’000 per annum; c = £’00,000;

standard errors in parentheses; Significance: ∗ = 10%; ∗∗ = 5%; ∗∗∗ = 1%

For equation (12) which relates to the retrospective assessment of change, the coefficients

of the transient life-event variables and changes in income and housing equity should be

interpreted as θ6 = (δ1 − δ2)/S2, where δ1 and δ2 capture their temporary effects on the

adjustment processes (5) and (7). There are significant negative coefficients for the events of

retirement and childbirth, for which there were no significant transient effects in the equation

for FWB1, implying positive coefficients in δ2. This means that occurrence of retirement

or childbirth during the intervening period makes the past appear (temporarily) financially

rosier from today’s perspective than it did at the time. Conversely, the large positive income

coefficient in θ6 and the small, marginally significant effect of income change in the model

for FWB1 implies that a rise in income has the temporary effect of making the past seem

worse than it did at the time – which is consistent with the adaptation hypothesis, only in

20

a transient sense.10

5 Conclusions

There is a widely-accepted view that the concept of welfare needs to be conceived much

more broadly than than conventional income- or expenditure-based microeconomic defini-

tions. Empirical implementation of these broader concepts generally involves the use of

‘subjective’ survey measures, like the two BHPS financial wellbeing variables used here: one

an assessment of current wellbeing, the other an evaluation of the direction of change over

the preceding year. Our findings suggest very strongly that the current variable should not

be regarded as a direct observation on wellbeing and that the retrospective variable is not

very reliable as an indicator of change. We have demonstrated the importance of dynamic

adjustment of perceived wellbeing, in two dimensions of time.

First, perceptions of current wellbeing take time to adjust fully to changed circumstances:

only around two-thirds of the year-to-year adjustment that would be required to bring per-

ceived wellbeing in line with changed circumstances is accomplished within a year and there

is evidence of a substantial transient over-reaction to major life events like unemployment,

onset of long-term ill-health and booms in the housing market, in their year of occurrence.

Second, memory operates in a non-stationary way, so that perceptions of wellbeing,

as experienced at some fixed time in the past, may vary depending when the perception

is expressed. In particular, perceptions of past wellbeing are positively contaminated by

current circumstances, suggesting a process of memory substitution: that difficulty in recall

leads to some degree of substitution of the current state for the past state, when forming

perceptions of the past. This is the opposite effect to that produced by the much-discussed

adaptation hypothesis, which would lead to a negative influence of current wellbeing on

10For other coefficients in θ5 and θ6, where both are significant and of the same sign, it is not possible todraw definite conclusions about the sign of δ2, since θ5 and θ6 have different normalisations.

21

today’s judgement of the past. We have also found transient effects of major events on

recollections of past wellbeing.

Despite these large dynamic distortions detectable in individual sequences of reported

perceptions of wellbeing, it is possible to uncover an underlying wellbeing measure, using

appropriately specified dynamic models. This reveals, in addition to significant income

effects, important long-term roles for human capital, relationship status, housing wealth and

demographic characteristics, which suggest that the financial wellbeing variables succeed in

capturing a wider concept of welfare than income alone, perhaps approximating to Sen’s

notion of the individual’s “entitlements” set.

References

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24

Appendix 1: Identification and Estimation

A1.1 A general model

In terms of the underlying continuous variables, tzt and (tzt−1 − t−1zt−1), the model of section3 is a multi-equation first-order vector autoregression, with a latent moving average component: aVARMA(1,1) system. Generalise this to a J-equation system for a panel of individuals indexed byi = 1...n, with unobservable individual effects and a non-degenerate Q-dimensional moving averagecomponent:

y∗jit =J

∑

k=1

αjky∗

kit−1 + x′

itβj + uji +

Q∑

q=1

(κ0jqζqit + κ1jqζqit−1) + εjit , j = 1...J (13)

or, in matrix form:y∗it = Ay∗it−1 +Bxit + ui +K0ζit +K1ζit−1 + εit (14)

where A = αjk, B = β1...βJ, K0 = κ0jk, K1 = κ1jk. Since K0 and K1 are unrestrictedin scale, ζit can be normalised to have unit variances. The J-dimensional vectors y∗it and ui havetypical jth elements y∗jit and uji and ζit is Q-dimensional, with elements ζqit. Note that (11)-

(12) imply nonlinear restrictions on the elements of B, K0 and K1 in (14). These restrictions areimposed, rather than leaving B, K0 and K1 unconstrained, to avoid an unduly high-dimensionalparameter space. We assume the vectors ui , ζi0, ..., ζiTi

are mutually independent, with Gaussiandistributions:

ui ∼ N(0,Σu) (15)

ζit ∼ N(0, I) , t = 0...Ti (16)

We only observe each element of the vector y∗it according to the following grading scale:

yjit = r iff y∗jit ∈ [Γj−1r,Γjr) , j = 1...J ; r = 1...R (17)

where each Γj0 = −∞ and ΓjRj= +∞. Note that different variables may use scales with different

numbers and types of interval: in our case, with J = 2 equations, we have R1 = 5 and R2 = 3.The thresholds Γjr may be observable in some applications (such as banded earnings variables)or specified as unknown parameters for others (such as Likert responses). We are interested inthe latter case, which implies that the origin and scale of the latent vector y∗it are unobservable.Consequently normalisation restrictions are required. Common practice is to drop the interceptterm from the vector xit and set the residual variance to unity. For our purposes, these areinconvenient and we instead make the following observationally equivalent normalisation:

Γj1 = 0 ; Γj2 = 1 , j = 1...J (18)

Note that the use of this normalisation requires the inclusion of an intercept dummy variable in thecovariate vector xit. We deal with the initial conditions problem using the following approximation,which allows for both the random effect ui and the initial MA term ζi0 to influence yi0.

y∗i0 = Dwi +Gui +K0ζi0 + ηi (19)

where ηi is a random vector distributed as N(0,Ση), independently of ui and ζit for all t ≥ 0. Theunobserved y∗i0 is assumed to be mapped into the observable grades yi0 by the same mechanism(17), possibly allowing for different values of the thresholds Γjr to give additional flexibility. The

25

covariate vector wi should be specified sufficiently richly to give an adequate approximation and itshould include an intercept dummy variable.

The process (14) and approximation (19) imply a distributed lag representation of the form:

y∗it = AtDwi +t−1∑

s=0

AsBxit−s + λit (20)

where the stochastic error λit has the following structure:

λit =[

AtG+ St

]

ui +K0ζit +t−1∑

s=0

At−s−1 [K1 +AK0] ζis +t

∑

s=1

At−sεis +Atηi (21)

where St =∑t−1

s=0As = (I −A)−1 (

I −At)

.

A1.2 Identification

Consider the residual vector λit defined by (21) and write the initial period residual λi0 =Gui + ζi0 +ηi. Under our assumptions, these random vectors are jointly normal with covariances:

C00 = GΣuG′ +K0K

′

0 + Ση (22)

C0t = GΣu

[

AtG+ St

]

′

+ ΣηAt′ +K0 [K1 +AK0]

′At−1′ , t > 0 (23)

Cst = [AsG+ Ss]Σu

[

AtG+ St

]

′

+AsΣηAt′ +

s∑

j=1

As−jΣεAt−j ′

+δstK0K′

0 + (1 − δst)K0 [K1 +AK0]′At−s−1′

+s−1∑

j=0

As−j−1 [K1 +AK0] [K1 +AK0]′At−j−1′ , 0 < s ≤ t (24)

where Cst = cov(λis,λit), δst is the Kronecker delta and we use the convention that A0 = I in thecase of A = 0.

Now consider the following identification strategy. With the normalisations Γj1 = 0 and Γj2 = 1,a multivariate cross-section ordered probit of yi0 on wi for the initial period identifies D andC00. Now construct a set of variables yi0 = Dwi and estimate equation (20) for wave t = 1by regressing yi1 on yi0,xi1, using multi-equation ordered probit. For this to be possible, weneed the identifying assumption that Dwi and xi1 are non-collinear, which requires the presenceof sufficient variables in wi which are excluded from xi1. Estimation of this system for wave 1identifies A,B and C11. With A,B and D known, it is then possible to identify the covariancematrices Cst for all s, t from the residuals for periods s, t.

The next step is to identify G and Σu from the covariances Cst. Note that:

C0,t+1 −C0tA′ = GΣu , for any t ≥ 1 (25)

C1t −C1,t−1A′ = AGΣu + Σu , for any t ≥ 3 (26)

Consequently Σu is identifiable as C1t − C1,t−1A′ − A [C0,t+1 −C0tA

′] for any t ≥ 3. If Σu is

non-singular, then G is identified as [C0,t+1 −C0tA′]Σ−1

u .

26

Singularity of Σu would generally only arise when we specify a low-dimensional factor structureso that Σu is expressible as HΩuH

′ where Ωu is a k×k positive definite matrix with k < J and His a J × k matrix of rank k, subject to k2 normalisation restrictions to give a unique pair (H,Ωu).Then (25) can be rewritten as C0,t+1 − C0tA

′ = [GH] [ΩuH′] and solved for the product GH,

which is the J × k coefficient matrix of the k factors in the initial period.

The compound process vit = K0ζit +K1ζit−1 + εit is characterised fully by its variance and1st-order autocovariance matrices:

V ar (vit) = K0K′

0 +K1K′

1 + Σε (27)

Cov (vit,vit−1) = K1K′

0 (28)

When the MA process is unrestricted,K0,K1 and Σε cannot be identified from (27) and (28), sincealternative values

K+0 ,K+

1 ,Σ+ε

give exactly the same autocovariances, where K+0 = cK0,K

+1 =

c−1K1 and Σ+ε = Σε + (1− c2)K0K

′

0 + (1− c−2)K1K′

1, for any positive constant c such that Σ+ε

is positive definite. In our two-equation application based on (11)-(12), we resolve this by usingthe normalisation κ01 = 1, leaving κ02, κ11 and κ12 unrestricted. The parameters κ02, κ11 and κ12

can be derived uniquely from knowledge of K0K′

1 (provided either κ11 6= 0 or κ12 6= 0), which canbe constructed as C01 −GΣu (I +AG)′ − [C00 −GΣuG]A′

The final step is to recover Ση and Σε. The former can be constructed, using (22), as C00 −GΣuG

′ −K0ΣζK0′. The latter is given directly by (24) for s = t = 1 as:

Σε = C11 − [I +AG]Σu [I +AG]′ −K0ΣζK′

0 − [K1 +AK0] [K1 +AK0]′ −AΣηA

′ (29)

A1.3 Maximum simulated likelihood estimation

The full model consists of equation (19) and a set of equations (20) for any collection of periodst > 0. In practice, the initial conditions model (19) is only an approximation and is a potentialsource of specification error. However, if A has stable roots so that At → 0 as t increases, thenthe influence of the initial conditions declines as we consider later periods. There is, therefore, acase for leaving a gap (of S periods) between the initial period 0 and the subsequent periods usedto estimate the model (20). Thus we work with a system of J(T − S + 1) equations consisting of(19) and (20) for t = S + 1...T . Data on yi1...yiS are not used but we do require observationson xi1...xiS spanning the omitted periods. The choice of S involves a trade-off between possiblemisspecification bias and efficiency, since increasing S reduces the influence of initial conditionsbut also reduces the number of observations used for estimation. Increasing S also reduces thedimensionality of the computational problem.

Let the observed outcome for yjit be rjit, implying y∗jit ∈[

Γj,rjit−1,Γj,rjit

)

. The likelihood forthis set of events is:

Pr (yjit = rjit, j = 1...J ; t ∈ T|wi,xi1...xiT )

= Pr(

λjit ∈[

Γj,rjit−1 − µjit,Γj,rjit− µjit

)

, j = 1...J ; t ∈ T)

(30)

where T is the index set 0, S + 1...T, λjit is the residual for equation j at individual i and time t

and µjit is the jth element of the vector µit = AtDwi +∑t−1

s=0AsBxit−s. The covariance matrix of

the residual vector for individual i) has a block structure, with blocks given by expressions of theform (22)-(24). The probability (30) is a J(T − S + 1)-dimensional rectangle probability. Undernormality, probabilities of this kind can be approximated using the GHK simulator (Hajivassiliouand Ruud, 1994), leading to a simulated log-likelihood function:

lnL (θ, R) =n

∑

i=1

ln P (θ, R) (31)

27

where P (θ, R) is the predicted probability (30) for individual i, estimated using the GHK algorithmwith R replications. Note that, since y∗2it−1 does not appear in (11)-(12), y∗2i0 is not required, soonly a single initial condition has to be modelled.

Techniques such as antithetic acceleration or Halton sequences can be used to improve simu-lation precision. We use a three-stage computational scheme. First, an initial approximation tothe ML estimate is calculated, using crude Monte Carlo simulation with R = 20 replications toconstruct the likelihood (31), which is maximised numerically with respect to the parameters θ.At the second stage, the number of replications is increased to 200: 100 pseudo-random draws andtheir antithetics.11 The resulting simulated likelihood is maximised numerically. At the third stage,a final evaluation of the log likelihood and its gradient vector is made with R = 1000 replications tocheck on simulation error and make a 1-iteration update on the converged point. In the applicationreported below, we use a skip rate of S = 5, giving a maximum dimension of 11 for the rectangleprobabilities to be simulated. For optimisation, we use the simulated annealing algorithm (Goffeet al 1994) as implemented in a Gauss routine written by E.G.Tsionas to produce a starting pointfor a quasi-Newton algorithm implemented in the Gauss MAXLIK routine.

11The 100 antithetics are replaced by fresh pseudo random draws in the 27% of cases where antitheticsproduce no reduction in the simulation variance.

28

Appendix 2: Full parameter estimates

Table A1 Random effects ordered probit models forsatisfaction with life overall (SLO) and income (SI)

Covariate SLO SI

Financial wellbeing level 2 0.394∗∗∗ 0.443∗∗∗

(0.069) (0.073)Financial wellbeing level 3 0.764∗∗∗ 1.331∗∗∗

(0.063) (0.068)Financial wellbeing level 4 1.039∗∗∗ 2.176∗∗∗

(0.065) (0.070)Financial wellbeing level 5 1.275∗∗∗ 2.805∗∗∗

(0.067) (0.071)Gross household income per head -0.000 0.022∗∗∗

(0.001) (0.002)Personal share in household income −0.081∗ −0.104∗∗

(0.047) (0.045)Change in income in last year -0.000 −0.007∗∗∗

(0.001) (0.001)Female -0.070 0.092∗∗

(0.045) (0.037)Afro-Caribbean 0.244 0.266

(0.198) (0.178)South Asian 0.203 0.023

(0.185) (0.167)In relationship 0.292∗∗∗ 0.016

(0.061) (0.053)Divorced/separated -0.080 −0.174∗∗∗

(0.070) (0.061)Widowed 0.083 0.125∗

(0.077) (0.067)Employed -0.016 0.179∗∗∗

(0.047) (0.045)Self-employed -0.016 0.247∗∗∗

(0.060) (0.057)Retired -0.042 0.001

(0.072) (0.068)Unemployed −0.252∗∗∗ −0.466∗∗∗

(0.085) (0.086)Long-term sick −0.666∗∗∗ −0.253∗∗∗

(0.072) (0.069)Degree −0.295∗∗∗ -0.001

(0.068) (0.058)HND/HNC −0.132∗ 0.171∗∗

(0.079) (0.069)A-levels −0.253∗∗∗ -0.037

(0.063) (0.055)O-levels −0.099∗ -0.003

(0.053) (0.044)Vocational qualifications 0.019 −0.062∗

(0.043) (0.036)

29

Table A1 continued

Covariate SLO SI

Number pre-school children -0.049 0.015(0.064) (0.062)

Number school-age children −0.042∗∗ 0.058∗∗∗

(0.018) (0.017)Number retired household members -0.024 0.023

(0.044) (0.042)Number working-age household members −0.061∗∗∗ -0.009

(0.021) (0.020)Has pre-school children 0.025 0.123

(0.081) (0.078)ownocc 0.088∗∗ 0.119∗∗∗

(0.043) (0.039)Private rented housing 0.207∗∗∗ 0.134∗∗

(0.059) (0.054)Birth year −0.013∗∗∗ −0.020∗∗∗

(0.002) (0.002)Birth year squared 0.000 0.001∗∗∗

(0.000) (0.000)Separated/divorced in last year −0.332∗∗∗ 0.043

(0.088) (0.086)Widowed in last year −0.592∗∗∗ 0.106

(0.134) (0.129)Retired in last year 0.239∗∗∗ 0.060

(0.078) (0.073)Entered unemployment in last year 0.014 0.100

(0.114) (0.117)Became long-term sick in last year −0.245∗ -0.126

(0.139) (0.143)New child in last year 0.154∗∗ 0.012

(0.063) (0.061)Threshold 1 −2.426∗∗∗ -0.126

(0.123) (0.117)Threshold 2 −1.882∗∗∗ 0.553∗∗∗

(0.121) (0.118)Threshold 3 −1.135∗∗∗ 1.353∗∗∗

(0.121) (0.118)Threshold 4 −0.246∗∗ 2.266∗∗∗

(0.120) (0.118)Threshold 5 1.001∗∗∗ 3.385∗∗∗

(0.121) (0.119)Threshold 6 2.514∗∗∗ 4.511∗∗∗

(0.121) (0.119)Intra-class correlation 0.541∗∗∗ 0.426∗∗∗

(0.008) (0.009)

30

Table A2 Transition rates for the current state of financial wellbeing

Destination state AllOrigin Very Quite Getting Doing Living desti-state difficult difficult by alright comfortably nations

Verydifficult 32.9 26.6 29.5 9.2 1.9 2.8

Quitedifficult 10.6 25.5 47.5 13.3 3.1 6.0

Gettingby 2.5 8.8 54.3 26.3 8.1 27.9

Doingalright 0.5 1.8 19.5 53.5 24.7 32.2

Livingcomfortably 0.2 0.5 6.3 24.0 68.9 31.0

All origins 2.5 5.6 27.3 33.0 31.7 100.0

Note: Row percentages: BHPS sample of individuals who were household referencepersons in 1992, using waves from 1992-2003, n = 43, 594)

31

Table A3 Summary statistics for covariates

Variable Mean 1993-2003

Female 0.403African/Afro-Caribbean 0.007South Asian 0.010Any pre-school child in household 0.107Number of pre-school children 0.134Number of school-age children 0.458Number of retired household members 0.433Number of other adults 1.468Married or cohabiting 0.649Divorced or separated 0.107Widowed 0.141Employed 0.458Self-employed 0.085Retired 0.308Unemployed 0.029Long-term sick 0.047(Year of birth - 1940)/10 0.314Degree 0.113Higher diploma or certificate 0.070Higher school qualification (A-levels) 0.141Intermediate school qualifications (O-levels/GCSE) 0.258Vocational qualifications 0.340Homeowner 0.730Private rental housing 0.066Housing equity (£’00,000) 0.578Per capita gross annual household income (£’000) 11.1Respondent’s share of household income 0.654Divorced or separated in last year 0.008Widowed in last year 0.004Retired in last year 0.013Lost job in last year 0.010Onset of long-term illness in last year 0.004Birth of child in last year 0.023Change in real per capita household income 0.154Change in real housing equity 0.048

32

Table A4 MSL estimates of joint model: adjustment parameters, long-run effects ψ/S1

and transient effects θ5 and θ6 (standard errors in parentheses)

Parameter Estimate Parameter Estimate Parameter Estimate

λ 0.6654 A-level 0.1949 2001 -0.0979(0.02) (0.0784) (0.0528)

φS1/S2 0.0904 O-level 0.1819 2002 -0.1024(0.0359) (0.0647) (0.0554)

(λ − π)S1/S2 -0.028 Vocational education 0.0341 Newly-divorced -0.1879(0.0252) (0.052) (0.1195)

Constant 1.9366 No. pre-school children -0.1459 Newly-widowed 0.162(0.1762) (0.1277) (0.1783)

Female 0.1397 No. school-age children 0.0006 Newly-retired -0.1086(0.0549) (0.0285) (0.0995)

Black -0.7534 No. retired 0.0609 Job loss -0.5711(0.3207) (0.0736) (0.1734)

South Asian -0.446 No. other adults -0.0632 Onset of illness -0.6238(0.2187) (0.0376) (0.1765)

Married/cohabiting 0.3979 Any pre-school children 0.2342 New birth -0.0897(0.0888) (0.1669) (0.1112)

Divorced/separated -0.2887 Home-owner 0.6288 ∆ income -0.2608(0.097) (0.0685) (0.1375)

Widowed 0.016 Private rental 0.0963 ∆ housing equity 0.0987(0.1024) (0.0967) (0.0495)

Employed -0.0676 Housing equity 0.053 Newly-divorced -0.1952(0.0828) (0.0152) (0.0705)

Self-employed -0.0978 Annual household income 4.5794 Newly-widowed 0.029(0.1048) (0.2456) (0.1057)

Retired -0.1302 Share in income 0.2523 Newly-retired -0.2836(0.1233) (0.0861) (0.0539)

Unemployed -0.619 Birth year/10 -0.2463 Job loss -0.5059(0.1846) (0.0279) (0.0748)

Long-term sick -0.4532 (Birth year/10)2 0.0127 Onset of illness -0.0662(0.1239) (0.0104) (0.103)

Degree 0.3286 1999 -0.343 New birth -0.2105(0.0796) (0.0709) (0.0527)

Diploma/certificate 0.3734 2000 -0.3079 ∆ income 0.9381(0.0994) (0.0539) (0.1449)

∆ housing equity 0.1581(0.0165)

33

Table A4 continued MSL estimates of joint model: initial condition coefficients, covarianceparameters and ordinal thresholds (standard errors in parentheses)

Parameter Estimate Parameter Estimate Parameter Estimate

Constant 1.2739 No. other adults2 0.1543 No. other adults -0.2992(0.27250001) (0.0634) (0.0974)

Female 0.0748 Pre-school children -0.0079 Home-owner 0.6298(0.068) (0.1782) (0.1998)

Black -0.8267 Home-owner -0.1337 Private rental 0.4036(0.26910001) (0.1725) (0.2242)

South Asian -0.7811 Private rental -0.1425 Housing equity -0.0911(0.2369) (0.1737) (0.0811)

Married/cohabiting 0.3261 Housing equity 0.2911 Household income 3.446(0.17460001) (0.0991) (0.7498)

Divorced/separated -0.0973 Household income 4.9309 Share in income -0.1106(0.21089999) (0.6052) (0.2269)

Widowed 0.2994 Share in income 0.3088 G11 1.1786(0.26530001) (0.1498) (0.1042)

Employed 0.3811 (Birthyear-1940)/10 -0.1579 G12 -0.7142(0.1224) (0.0347) (0.0873)

Self-employed 0.1771 ((Birthyear-1940)/10)2 0.0358 σu1 0.633(0.1803) (0.0111) (0.0765)

Retired 0.1277 Married/cohabiting 0.0648 ρu1u2 0.3920(0.2045) (0.2098) (0.0473)

Unemployed -0.2765 Divorced/separated -0.4439 σu2 0.3169(0.1578) (0.2452) (0.0187)

Long-term sick 0.083 Widowed -0.2904 σε1 0.4988(0.1981) (0.2834) (0.1653)

Degree 0.0524 Employed -0.4121 ρε1ε2 0.7386(0.1025) (0.1882) (0.1756)

Diploma/certificate 0.1985 Self-employed -0.4023 σε2 0.3559(0.1135) (0.2522) (0.0066)

A-level 0.2664 Retired -0.2301 ση 0.6332(0.0899) (0.2805) (0.2071)

O-level 0.0692 Unemployed -0.5826 Γ13 2.792

(0.0707) (0.3239) (0.0798)

Vocational education 0.0175 Long-term sick -0.5009 Γ14 4.3878

(0.058) (0.2585) (0.1417)

No. pre-school children -0.1032 No. pre-school children 0.3337 Γ03 2.694

(0.1434) (0.1326) (0.1041)

No. school-age children 0.125 No. school-age children 0.0101 Γ04 3.9236

(0.067) (0.0869) (0.1684)

No. retired 0.0255 No. retired -0.0125 σζ 1.2418(0.1383) (0.1784) (0.3674)

34